TY - JOUR
ID - 24696
TI - Parameters of the coprime graph of a group
JO - International Journal of Group Theory
JA - IJGT
LA - en
SN - 2251-7650
AU - Hamm, Jessie
AU - Way, Alan
AD - Department of Mathematics, Winthrop University, 142 Bancroft Hall Rock Hill, SC, USA
Y1 - 2021
PY - 2021
VL - 10
IS - 3
SP - 137
EP - 147
KW - coprime graph
KW - Finite groups
KW - Independence number
KW - perfect graph
DO - 10.22108/ijgt.2020.112121.1489
N2 - There are many different graphs one can associate to a group. Some examples are the well-known Cayley graph, the zero divisor graph (of a ring), the power graph, and the recently introduced coprime graph of a group. The coprime graph of a group $G$, denoted $\Gamma_G$, is the graph whose vertices are the group elements with $g$ adjacent to $h$ if and only if $(o(g),o(h))=1$. In this paper we calculate the independence number of the coprime graph of the dihedral groups. Additionally, we characterize the groups whose coprime graph is perfect.
UR - https://ijgt.ui.ac.ir/article_24696.html
L1 - https://ijgt.ui.ac.ir/article_24696_9bdd71ba7326bf96ac429abd41fd0412.pdf
ER -